Star Polymers in Good Solvents From Dilute to Concentrated Regimes: Crossover Approach

Abstract

An introduction is given to the crossover theory of the conformational and thermodynamic properties of star polymers in good solvents. The crossover theory is tested against Monte Carlo simulation data for the structure and thermodynamics of model star polymers. In good solvent conditions, star polymers approach a "universal" limit as N → ∞ ; however, there are two types of approach towards this limit. In the dilute regime, a critical degree of polymerization N * is found to play a similar role as the Ginzburg number in the crossover theory for critical phenomena in simple fluids. A rescaled penetration function is found to control the free energy of star polymer solutions in the dilute and semidilute regions. This equation of state captures the scaling behaviour of polymer solutions in the dilute/semidilute regimes and also performs well in the concentrated regimes, where the details of the monomer-monomer interactions become important.

Scaling of Star Polymers with 1−80 Arms

“…Unfortunately, they did not give predictions for A f , so we cannot make a detailed comparison with our data. But we should point out that [13,14] also obtained much less swelling with f than predicted in Refs. [9,11,12].…”

“…free) chains [8] or on heuristic assumptions [9,10]. There exist several renormalization group calculations, but those not based heavily on simulation data [11,12] seem to describe some of the data rather poorly, and Monte Carlo simulations are needed to fix free parameters in such theories [13,14].…”

Hydrogen‐Bonded Complexes of Star Polymers

“…Indeed, while number of repeat units in lPEO and sPEO are similar (N PEO = 273 and 295, respectively), the linear chain spreads out over a volume that is ≈50% larger than that occupied by a more compact star PEO. [8,18] Correspondingly, density of PEO oxygen atoms serving as acceptors in hydrogen bonding with PMAA carboxylic groups is higher for sPEO. The average number of hydrogen bonds per PMAA between carboxylic hydrogens of PMAA and oxygens of PEO (n PMAA-PEO ) can be estimated using the following equation…”

“…Indeed, while number of repeat units in l PEO and s PEO are similar ( N PEO = 273 and 295, respectively), the linear chain spreads out over a volume that is ≈50% larger than that occupied by a more compact star PEO. [ 8,18 ] Correspondingly, density of PEO oxygen atoms serving as acceptors in hydrogen bonding with PMAA carboxylic groups is higher for s PEO. The average number of hydrogen bonds per PMAA between carboxylic hydrogens of PMAA and oxygens of PEO ( n PMAA‐PEO ) can be estimated using the following equation where Δ F PMAA − PEO / kT is free energy change upon formation of a hydrogen bond between PMAA and PEO, is number of free carboxylic hydrogens in a PMAA chain (i.e.,) that do not participate in hydrogen bonding with another carboxylic group, or water or a different oxygen of PEO, is number of free oxygens (i.e., , oxygens that are not hydrogen bonded with water or another carboxylic group), N PEO chains / V is the number of PEO chains per unit volume, and V PEO chain is the volume of a PEO chain.…”

“…[6] The contraction factor progressively decreases with an increase in number of arms, leading to highly compact structures with increased average segmental densities for polymer stars with large number of arms N, with a predicted crossover from a polymer-like to a particlelike behavior at N > 6. [5,[7][8][9] The star architecture also results in highly nonuniform distribution of segmental densities and relaxation times, with motions of the units close to the core being restricted by the segmental crowding near the core. [10] As a result, star polymers with large number of arms exhibit long relaxation times in melts -an effect that is especially pronounced for polymers with large number of arms and low molecular weight.…”